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Spreading of quasimodes in the Bunimovich stadium

Burq, Nicolas; Hassell, Andrew; Wunsch, Jared

Description

We consider Dirichlet eigenfunctions uλ of the Bunimovich stadium S, satisfying (∆ − λ²)uλ = 0. Write S = R ∪ W where R is the central rectangle and W denotes the “wings,” i.e., the two semicircular regions. It is a topic of current interest in quantum theory to know whether eigenfunctions can concentrate in R as λ → ∞. We obtain a lower bound Cλ⁻² on the L² mass of uλ in W, assuming that uλ itself is L²-normalized; in other words, the L² norm of uλ is controlled by λ2 times the L² norm...[Show more]

CollectionsANU Research Publications
Date published: 2007
Type: Journal article
URI: http://hdl.handle.net/1885/100255
Source: Proceedings of the American Mathematical Society
DOI: 10.1090/S0002-9939-06-08597-2

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